#14514906

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁶

Aliases

No aliases for this group.

Splittings

Fitting

C₂×D₄ ⋊ S₅

Subgroups

	subgroup	G/H
center, Frattini	C₂	C₂³×S₅
commutator, socle, cosocle	C₂×A₅	C₂⁴
Fitting, hypercenter	C₂×D₄	S₅
hypocenter	A₅	H(5,𝔽₂)
LCS	G ▷ C₂×A₅ ▷ A₅
UCS	C₁ ◁ C₂ ◁ C₂×D₄

1525 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 1525 conjugacy classes of subgroups — too many to draw. Only its 85 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 40

Permutation generators:

(3,4,5)(6,37,7,36)(8,34,9,35)(10,32,11,33)(12,31,13,30)(14,28,15,29)(16,27,17,26)(18,25,19,24)(20,22,21,23);(1,4)(6,14)(7,15)(8,16)(9,17)(10,19)(11,18)(12,21)(13,20)(22,30)(23,31)(24,32)(25,33)(26,35)(27,34)(28,37)(29,36);(1,3,5)(2,4)(6,23)(7,22)(8,24)(9,25)(10,27)(11,26)(12,28)(13,29)(14,30)(15,31)(16,33)(17,32)(18,34)(19,35)(20,37)(21,36);(1,2,3,4,5)(6,34)(7,35)(8,37)(9,36)(10,31)(11,30)(12,32)(13,33)(14,27)(15,26)(16,28)(17,29)(18,22)(19,23)(20,25)(21,24)

Conjugacy classes & character table

61 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 240604);